How could we compute the length of a list? Without worrying yet about what lambda-calculus implementation we're using for the list, the basic idea would be to define this recursively:

@@ -211,7+220,8 @@ Instead of writing out a long formula twice, we could write:

and the initial `(\x. x x)` is just what we earlier called the <code>&omega;</code> combinator (lower-case omega, not the non-terminating <code>&Omega;</code>). So the self-application of `H` can be written:

and this will indeed implement the recursive function we couldn't earlier figure out how to define.

@@ -414,7+424,7 @@ to *the tail* of the list we were evaluating its application to at the previous

##Fixed-point Combinators Are a Bit Intoxicating##

-![tatoo](/y-combinator.jpg)

+![tatoo](/y-combinator-fixed.jpg)

There's a tendency for people to say "Y-combinator" to refer to fixed-point combinators generally. We'll probably fall into that usage ourselves. Speaking correctly, though, the Y-combinator is only one of many fixed-point combinators.